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I was creating a map of Italy and I noticed a problem. The provinces I created have pratically no population and no economy. How can it be possible that Rome have 488 inhabitants and 300 of economy... even in the Middle Ages it was not so low. How can I fix this?

Welcome, I'd want this thread to be widespread because it containts a potential milestone in the history of the post-release AoC2 development. Łukasz, please do leave a note so I can know you are reading this.
Economy in this game is fun but probably unattended by most players part of the game. And it is most likely to stay this way due to the fact, that it is also an extremely tiring process, which requires you to move your mouse like a mad man and click like some furious asian in dota.
Let me tell you what you have to do in order to increase Economy, Development, Stability or Happiness in a single province. Here's what I do:
Look at the bottom-left panel of the screen. Click a desired icon. I'll go for Development.
Now you see a list of your provinces with their state. Now click on one of them twice.
Move the slider all the way to the right side and confirm.
Repeat all above for every province until your treasury is empty or you run out of movement points, click next turn.
Repeat all above, continue until you maxed out all your provinces or you die of old age.
This looks terrible when you read it, and it is just as terrible in-game as you would expect. Now let me tell you how I imagine it should be done:
Again - Look at the bottom-left panel of the screen. Click a desired icon.
List pops up but you can also interact with the map.
You want to quickly fill the province with maximum amount of investment you are allowed to do using the slider, but withous using the slider. You click the Left Shift and on each province a pop up is displayed showing you the cost of that operation. Click Left Shift+LMB and it's done. This way you can swiftly boost multiple provinces in under 5 seconds.
Why do I find it important? Because let me tell you - it's fun, it's faster than conquering and having 300 000 Economy doesn't leave you with 1000 Economy in each of your 300 provinces. Instead you have 20 provinces with 15 000 Economy each.
It is too hard to acquire population
Wars between two superpowers or atleast powers of equal strenght requires enlisting large portions of population, leaving all of your border provinces empty.
Let's say that two empires of 500 000 men fought a war. They enlisted a total of 50 000 men each, and now both of them have 450 000 pop. Now these men will probably never be regained, because the growth is so incredibly slow, that the exploited provinces will be forever wastelands.
Here's what I suggest you should do:
There should be a way to invest in Immigration. Immigrants will quickly fill your empty provinces, but not with native population. As a result, the province Stability will decrease, but there is a fix to that already in the game.
Immigration max investment per turn should not be based on the current state of population, but on the province's Economy.
This text has been copied directly from my thread on Steam where no official answer had been received.
https://steamcommunity.com/app/603850/discussions/0/3315110799624261356/

I can't figure out what investing in the development of a province actually accomplishes. It has no noticeable effect on Tax income, nor on Production income. You can invest thousands of gold into a province but not, as far as I can tell, actually gain anything from it except a slight increase in Administrative costs.
Is there some important game mechanic I'm missing here? What does the "Development" level of a province do?

How I Found This Feature
I was making a mod where there was real world alliances. While doing this I realized that NATO was way too OP! I decided to go on a journey to find how to make countries like, Russia and China stronger. I figured out some things without help but was never able to share this in which a update deleted my mod. A few weeks later I come to this cite to share my wonderful information to the hungry and desiring community that likes timelaspes!
Tutorial
1. Go to "Events" on the main editor page.
2. Add a new event and do whatever recipient you want.
3. change to starting date to whatever date you want (if you want it to start instantly in-game.
4. Go to "Triggers" and click on "If Civilization Exist's" then click on any civilization that is currently in the scenario.
5. Go to "Outcome" and scroll down to economy. Do any country you want and scroll the economy anything you want it to be.
6. Add the provinces you want the economy to be in.
7. Go back and press "Save Event".
Copying the Tutorial
Dont copy the tutorial please! Im talking to you Raider Knight!☹️

I have been doing a bunch of tests on the economic system in order to figure out how things work and how best to increase a nation's wealth.
In the Budget screen, I set "Investments" to 100% and monitored the Economy levels and income growth of my country for 5 turns. I then spent 20 un-used Tech Points and put them all in "Economic Growth". The results of a +15% increase to Economic growth?
Rate of Economy growth: unchanged*
Cost of investing directly in a Province's Economy: unchanged
Rate of Development growth: unchanged (Curiously, the development growth rate correlates EXACTLY with the "Province Growth Rate", which I would think should affect population not development...)
Putting tech points into "Economic Growth" seems to have absolutely no effect whatsoever.
I think you have a bug.**
*Update: I did further testing to try to factor out the high randomness of Econ construction (Varying from +150 to +250 on any given turn with similar funding), and it appears that there WAS in fact a 15% increase in Econ growth. I apologize for the incorrect report. Randomness makes finding bugs hard!
**I'm still not convinced that everything with "Investment" is working properly, so I'll keep checking things.